Honors Geometry Sections 7.5 & 7.6 Surface Area & Volume of Cones & Spheres

Rather than giving the definition of a cone, let’s identify the parts of a cone. vertex slant height altitude/height radius lateral area base

Lateral Area of a Right Cone (L) = Surface Area of a Right Cone )S) = Volume of a Right Cone (V) = ½ x circumference x slant height = Lateral area + area of the base = 1/3 x area of base x height =

Example 1: Find the surface area and volume of a cone with a radius of 5 in. and a slant height of 13 in.

A sphere is the set of points in space that are the same distance, r, from a given point, called the center of the sphere.

The Surface Area of a Sphere (S) = _____ The Volume of a Sphere (V) = ___________

Example: The envelope of a hot-air balloon is a sphere 54 feet in diameter when inflated. The cost of the fabric used to make the envelope is $1.31 per square foot. Find (a) the cost of the balloon’s fabric and (b) the volume of air needed to expand the envelope to its full size.